Finite element, least squares and domains decomposition methods for the numerical solution of nonlinear problems in fluid dynamics
Abstract
Attention is given to fluid dynamicsrelated methods developed in recent years, some of which are of industrial interest; typically, these methods employ finite element approximations in order to handle complex geometries and nonlinear least squares formulations to treat nonlinearities. Conjugate gradient methods with scaling then solve the least squares problems, and subdomain decomposition is applied to reduce the solution of very large problems to that of problems of the same type but smaller domains. This decomposition approach allows the use of vector processors. Application of these methods to transonic flow calculations, to the numerical solution of the timedependent NavierStokes equations for incompressible viscous fluids, and in the numerical solution of partial differential equation problems by domain decomposition, are presently noted.
 Publication:

NASA STI/Recon Technical Report A
 Pub Date:
 December 1985
 Bibcode:
 1985STIA...8629472G
 Keywords:

 Computational Fluid Dynamics;
 Finite Element Method;
 Least Squares Method;
 Nonlinear Equations;
 Computerized Simulation;
 Conjugate Gradient Method;
 Incompressible Fluids;
 NavierStokes Equation;
 Numerical Flow Visualization;
 Partial Differential Equations;
 Transonic Flow;
 Viscous Fluids;
 Fluid Mechanics and Heat Transfer